Model predictive control systems and methods for internal combustion engines

ABSTRACT

An engine control method includes: generating a first predicted engine output torque and a first predicted mass of air per cylinder (APC) based on a model of the spark ignition engine and a first set of possible target values determined based on an engine torque request; generating a second predicted engine output torque and a second predicted mass of APC based on the model of the spark ignition engine and a second set of possible target values determined based on the engine torque request; determining a first cost for the first set of possible target values; determining a second cost for the second set of possible target values; selecting one of the first and second sets based on the first and second costs; and setting target values based on the possible target values of the selected one of the first and second sets.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to U.S. patent application Ser. No. ______(HDP Ref. No. 8540P-001409) filed on [herewith], Ser. No. ______ (HDPRef. No. 8540P-001410) filed on [herewith], Ser. No. ______ (HDP Ref.No. 8540P-001411) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001412) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001413) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001417) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001418) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001426) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001427) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001428) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001429) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001430) filed on [herewith], Ser. No. ______ (HDP Ref. No.8540P-001431) filed on [herewith], and ______ (HDP Ref. No.8540P-001432) filed on [herewith]. The entire disclosures of the aboveapplications are incorporated herein by reference.

FIELD

The present disclosure relates to internal combustion engines and moreparticularly to engine control systems and methods for vehicles.

BACKGROUND

The background description provided here is for the purpose of generallypresenting the context of the disclosure. Work of the presently namedinventors, to the extent it is described in this background section, aswell as aspects of the description that may not otherwise qualify asprior art at the time of filing, are neither expressly nor impliedlyadmitted as prior art against the present disclosure.

Internal combustion engines combust an air and fuel mixture withincylinders to drive pistons, which produces drive torque. Air flow intothe engine is regulated via a throttle. More specifically, the throttleadjusts throttle area, which increases or decreases air flow into theengine. As the throttle area increases, the air flow into the engineincreases. A fuel control system adjusts the rate that fuel is injectedto provide a desired air/fuel mixture to the cylinders and/or to achievea desired torque output. Increasing the amount of air and fuel providedto the cylinders increases the torque output of the engine.

In spark-ignition engines, spark initiates combustion of an air/fuelmixture provided to the cylinders. In compression-ignition engines,compression in the cylinders combusts the air/fuel mixture provided tothe cylinders. Spark timing and air flow may be the primary mechanismsfor adjusting the torque output of spark-ignition engines, while fuelflow may be the primary mechanism for adjusting the torque output ofcompression-ignition engines.

Engine control systems have been developed to control engine outputtorque to achieve a desired torque. Traditional engine control systems,however, do not control the engine output torque as accurately asdesired. Further, traditional engine control systems do not provide arapid response to control signals or coordinate engine torque controlamong various devices that affect the engine output torque.

SUMMARY

A prediction module generates a first predicted engine output torque anda first predicted mass of air per cylinder (APC) based on a model of thespark ignition engine and a first set of possible target valuesdetermined based on an engine torque request and generates a secondpredicted engine output torque and a second predicted mass of APC basedon the model of the spark ignition engine and a second set of possibletarget values determined based on the engine torque request. A costmodule: determines a first cost for the first set of possible targetvalues based on a first predetermined weighting value, the firstpredicted engine output torque, the engine torque request, a secondpredetermined weighting value, and the first predicted mass of APC; anddetermines a second cost for the second set of possible target valuesbased on the first predetermined weighting value, the second predictedengine output torque, the engine torque request, the secondpredetermined weighting value, and the second predicted mass of APC. Aselection module selects one of the first and second sets based on thefirst and second costs and that sets target values based on the possibletarget values of the selected one of the first and second sets. Athrottle actuator module controls opening of a throttle valve based on afirst one of the target values.

In further features: a boost actuator module that controls opening of awastegate of a turbocharger based on a second one of the target values;an exhaust gas recirculation (EGR) actuator module that controls openingof an EGR valve based on a third one of the target values; and a phaseractuator module that controls intake and exhaust valve phasing based onfourth and fifth ones of the target values.

In still further features, the cost module determines the first costbased on: a first product of the first predetermined weighting value anda magnitude of a first difference between the first predicted engineoutput torque and the engine torque request; and a second product of thesecond predetermined weighting value and a second difference between thefirst predicted mass of APC and a predetermined minimum APC. The costmodule determines the second cost based on: a third product of the firstweighting value and a magnitude of a third difference between the secondpredicted engine output torque and the engine torque request; and afourth product of the second weighting value and a magnitude of a fourthdifference between the second predicted mass of APC and thepredetermined minimum APC.

In yet further features the cost module: determines the first cost basedon a sum of the first and second products; and determines the secondcost based on a sum of the third and fourth products.

In further features, the first predetermined weighting value is greaterthan the second predetermined weighting value.

In still further features, the selection module selects the first setwhen the first cost is less than the second cost, and the selectionmodule selects the second set when the second cost is less than thefirst cost.

In yet further features, the cost module: determines the first costfurther based on a third predetermined weighting value, a firstpredicted crankshaft angle where a predetermined percent of injectedfuel will be burned, a predetermined minimum crankshaft angle, and apredetermined maximum crankshaft angle; and determines the second costfurther based on the third predetermined weighting value, a secondpredicted crankshaft angle where the predetermined percent of injectedfuel will be burned, the predetermined minimum crankshaft angle, and thepredetermined maximum crankshaft angle.

In further features, the prediction module further: generates the firstpredicted crankshaft angle based on the model of the spark ignitionengine and the first set of possible target values; and generates thesecond predicted crankshaft angle based on the model of the sparkignition engine and the second set of possible target values.

In still further features, the cost module: determines the first costfurther based on a fourth predetermined weighting value, a firstpredicted coefficient of variation (COV) of indicated mean effectivepressure (IMEP), a predetermined minimum COV of IMEP, and apredetermined maximum COV of IMEP; and determines the second costfurther based on the fourth predetermined weighting value, a secondpredicted COV of IMEP, the predetermined minimum COV of IMEP, and thepredetermined maximum COV of IMEP.

In yet further features, the prediction module further: generates thefirst predicted COV of IMEP based on the model of the spark ignitionengine and the first set of possible target values; and generates thesecond predicted COV of IMEP based on the model of the spark ignitionengine and the second set of possible target values.

An engine control method includes: generating a first predicted engineoutput torque and a first predicted mass of air per cylinder (APC) basedon a model of the spark ignition engine and a first set of possibletarget values determined based on an engine torque request; generating asecond predicted engine output torque and a second predicted mass of APCbased on the model of the spark ignition engine and a second set ofpossible target values determined based on the engine torque request;determining a first cost for the first set of possible target valuesbased on a first predetermined weighting value, the first predictedengine output torque, the engine torque request, a second predeterminedweighting value, and the first predicted mass of APC; determining asecond cost for the second set of possible target values based on thefirst predetermined weighting value, the second predicted engine outputtorque, the engine torque request, the second predetermined weightingvalue, and the second predicted mass of APC; selecting one of the firstand second sets based on the first and second costs; setting targetvalues based on the possible target values of the selected one of thefirst and second sets; and controlling opening of a throttle valve basedon a first one of the target values.

In further features, the engine control method further includes:controlling opening of a wastegate of a turbocharger based on a secondone of the target values; controlling opening of an exhaust gasrecirculation (EGR) valve based on a third one of the target values; andcontrolling intake and exhaust valve phasing based on fourth and fifthones of the target values.

In still further features, the engine control method further includes:determining the first cost based on: (i) a first product of the firstpredetermined weighting value and a magnitude of a first differencebetween the first predicted engine output torque and the engine torquerequest; and (ii) a second product of the second predetermined weightingvalue and a second difference between the first predicted mass of APCand a predetermined minimum APC; and determining the second cost basedon: (i) a third product of the first weighting value and a magnitude ofa third difference between the second predicted engine output torque andthe engine torque request; and (ii) a fourth product of the secondweighting value and a magnitude of a fourth difference between thesecond predicted mass of APC and the predetermined minimum APC.

In yet further features, the engine control method further includes:determining the first cost based on a sum of the first and secondproducts; and determining the second cost based on a sum of the thirdand fourth products.

In further features, the first predetermined weighting value is greaterthan the second predetermined weighting value.

In still further features, the engine control method further includes:selecting the first set when the first cost is less than the secondcost; and selecting the second set when the second cost is less than thefirst cost.

In yet further features, the engine control method further includes:determining the first cost further based on a third predeterminedweighting value, a first predicted crankshaft angle where apredetermined percent of injected fuel will be burned, a predeterminedminimum crankshaft angle, and a predetermined maximum crankshaft angle;and determining the second cost further based on the third predeterminedweighting value, a second predicted crankshaft angle where thepredetermined percent of injected fuel will be burned, the predeterminedminimum crankshaft angle, and the predetermined maximum crankshaftangle.

In yet further features, the engine control method further includes:generating the first predicted crankshaft angle based on the model ofthe spark ignition engine and the first set of possible target values;and generating the second predicted crankshaft angle based on the modelof the spark ignition engine and the second set of possible targetvalues.

In further features, the engine control method further includes:determining the first cost further based on a fourth predeterminedweighting value, a first predicted coefficient of variation (COV) ofindicated mean effective pressure (IMEP), a predetermined minimum COV ofIMEP, and a predetermined maximum COV of IMEP; and determining thesecond cost further based on the fourth predetermined weighting value, asecond predicted COV of IMEP, the predetermined minimum COV of IMEP, andthe predetermined maximum COV of IMEP.

In still further features, the engine control method further includes:generating the first predicted COV of IMEP based on the model of thespark ignition engine and the first set of possible target values; andgenerating the second predicted COV of IMEP based on the model of thespark ignition engine and the second set of possible target values.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description, the claims and the drawings. Thedetailed description and specific examples are intended for purposes ofillustration only and are not intended to limit the scope of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an example engine systemaccording to the present disclosure;

FIG. 2 is a functional block diagram of an example engine control systemaccording to the present disclosure;

FIG. 3 is a functional block diagram of an example air control moduleaccording to the present disclosure; and

FIG. 4 includes a flowchart depicting an example method of controlling athrottle valve, intake and exhaust valve phasing, a wastegate, and anexhaust gas recirculation (EGR) valve using model predictive controlaccording to the present disclosure.

In the drawings, reference numbers may be reused to identify similarand/or identical elements.

DETAILED DESCRIPTION

An engine control module (ECM) controls torque output of an engine. Morespecifically, the ECM controls actuators of the engine based on targetvalues, respectively, based on a requested amount of torque. Forexample, the ECM controls intake and exhaust camshaft phasing based ontarget intake and exhaust phaser angles, a throttle valve based on atarget throttle opening, an exhaust gas recirculation (EGR) valve basedon a target EGR opening, and a wastegate of a turbocharger based on atarget wastegate duty cycle.

The ECM could determine the target values individually using multiplesingle input single output (SISO) controllers, such as proportionalintegral derivative (PID) controllers. However, when multiple SISOcontrollers are used, the target values may be set to maintain systemstability at the expense of possible fuel consumption decreases.Additionally, calibration and design of the individual SISO controllersmay be costly and time consuming.

The ECM of the present disclosure generates the target values usingmodel predictive control (MPC). More specifically, the ECM identifiespossible sets of target values based on an engine torque request. TheECM determines predicted parameters for each of the possible sets basedon the possible sets' target values and a mathematical model of theengine. For example, the ECM determines a predicted engine output torqueand a predicted air per cylinder (APC) for each of the possible sets oftarget values. The ECM may also determine one or more other predictedparameters for each possible set of target values.

The ECM may determine a cost associated with use of each of the possiblesets. The cost determined for a possible set increases as a magnitude ofa first difference between the predicted engine output torque determinedfor that possible set and the engine torque request increases and viceversa. The cost also increases as a magnitude of a second differencebetween the predicted APC determined for that possible set and zeroincreases and vice versa. The ECM may select the one of the possiblesets having the lowest cost. In various implementations, instead of orin addition to identifying possible sets of target values anddetermining the cost of each of the sets, the ECM may generate a surfacerepresenting the cost of possible sets of target values. The ECM maythen identify the possible set that has the lowest cost based on theslope of the cost surface.

In this manner, the ECM may select the one of the possible sets that ispredicted to most closely track the engine torque request whileminimizing the APC. Minimizing the APC may minimize fuel consumption.The ECM sets the target values for controlling the engine actuatorsusing the target values of the selected possible set.

Referring now to FIG. 1, a functional block diagram of an example enginesystem 100 is presented. The engine system 100 includes an engine 102that combusts an air/fuel mixture to produce drive torque for a vehiclebased on driver input from a driver input module 104. The engine 102 maybe a gasoline spark ignition internal combustion engine.

Air is drawn into an intake manifold 110 through a throttle valve 112.For example only, the throttle valve 112 may include a butterfly valvehaving a rotatable blade. An engine control module (ECM) 114 controls athrottle actuator module 116, which regulates opening of the throttlevalve 112 to control the amount of air drawn into the intake manifold110.

Air from the intake manifold 110 is drawn into cylinders of the engine102. While the engine 102 may include multiple cylinders, forillustration purposes a single representative cylinder 118 is shown. Forexample only, the engine 102 may include 2, 3, 4, 5, 6, 8, 10, and/or 12cylinders. The ECM 114 may instruct a cylinder actuator module 120 toselectively deactivate some of the cylinders, which may improve fueleconomy under certain engine operating conditions.

The engine 102 may operate using a four-stroke cycle. The four strokes,described below, may be referred to as the intake stroke, thecompression stroke, the combustion stroke, and the exhaust stroke.During each revolution of a crankshaft (not shown), two of the fourstrokes occur within the cylinder 118. Therefore, two crankshaftrevolutions are necessary for the cylinder 118 to experience all four ofthe strokes.

During the intake stroke, air from the intake manifold 110 is drawn intothe cylinder 118 through an intake valve 122. The ECM 114 controls afuel actuator module 124, which regulates fuel injection to achieve atarget air/fuel ratio. Fuel may be injected into the intake manifold 110at a central location or at multiple locations, such as near the intakevalve 122 of each of the cylinders. In various implementations (notshown), fuel may be injected directly into the cylinders or into mixingchambers associated with the cylinders. The fuel actuator module 124 mayhalt injection of fuel to cylinders that are deactivated.

The injected fuel mixes with air and creates an air/fuel mixture in thecylinder 118. During the compression stroke, a piston (not shown) withinthe cylinder 118 compresses the air/fuel mixture. A spark actuatormodule 126 energizes a spark plug 128 in the cylinder 118 based on asignal from the ECM 114, which ignites the air/fuel mixture. The timingof the spark may be specified relative to the time when the piston is atits topmost position, referred to as top dead center (TDC).

The spark actuator module 126 may be controlled by a timing signalspecifying how far before or after TDC to generate the spark. Becausepiston position is directly related to crankshaft rotation, operation ofthe spark actuator module 126 may be synchronized with crankshaft angle.Generating spark may be referred to as a firing event. The sparkactuator module 126 may have the ability to vary the timing of the sparkfor each firing event. The spark actuator module 126 may vary the sparktiming for a next firing event when the spark timing is changed betweena last firing event and the next firing event. The spark actuator module126 may halt provision of spark to deactivated cylinders.

During the combustion stroke, the combustion of the air/fuel mixturedrives the piston away from TDC, thereby driving the crankshaft. Thecombustion stroke may be defined as the time between the piston reachingTDC and the time at which the piston reaches bottom dead center (BDC).During the exhaust stroke, the piston begins moving away from BDC andexpels the byproducts of combustion through an exhaust valve 130. Thebyproducts of combustion are exhausted from the vehicle via an exhaustsystem 134.

The intake valve 122 may be controlled by an intake camshaft 140, whilethe exhaust valve 130 may be controlled by an exhaust camshaft 142. Invarious implementations, multiple intake camshafts (including the intakecamshaft 140) may control multiple intake valves (including the intakevalve 122) for the cylinder 118 and/or may control the intake valves(including the intake valve 122) of multiple banks of cylinders(including the cylinder 118). Similarly, multiple exhaust camshafts(including the exhaust camshaft 142) may control multiple exhaust valvesfor the cylinder 118 and/or may control exhaust valves (including theexhaust valve 130) for multiple banks of cylinders (including thecylinder 118). In various other implementations, the intake valve 122and/or the exhaust valve 130 may be controlled by devices other thancamshafts, such as camless valve actuators. The cylinder actuator module120 may deactivate the cylinder 118 by disabling opening of the intakevalve 122 and/or the exhaust valve 130.

The time when the intake valve 122 is opened may be varied with respectto piston TDC by an intake cam phaser 148. The time when the exhaustvalve 130 is opened may be varied with respect to piston TDC by anexhaust cam phaser 150. A phaser actuator module 158 may control theintake cam phaser 148 and the exhaust cam phaser 150 based on signalsfrom the ECM 114. When implemented, variable valve lift (not shown) mayalso be controlled by the phaser actuator module 158.

The engine system 100 may include a turbocharger that includes a hotturbine 160-1 that is powered by hot exhaust gases flowing through theexhaust system 134. The turbocharger also includes a cold air compressor160-2 that is driven by the turbine 160-1. The compressor 160-2compresses air leading into the throttle valve 112. In variousimplementations, a supercharger (not shown), driven by the crankshaft,may compress air from the throttle valve 112 and deliver the compressedair to the intake manifold 110.

A wastegate 162 may allow exhaust to bypass the turbine 160-1, therebyreducing the boost (the amount of intake air compression) provided bythe turbocharger. A boost actuator module 164 may control the boost ofthe turbocharger by controlling opening of the wastegate 162. In variousimplementations, two or more turbochargers may be implemented and may becontrolled by the boost actuator module 164.

An air cooler (not shown) may transfer heat from the compressed aircharge to a cooling medium, such as engine coolant or air. An air coolerthat cools the compressed air charge using engine coolant may bereferred to as an intercooler. An air cooler that cools the compressedair charge using air may be referred to as a charge air cooler. Thecompressed air charge may receive heat, for example, via compressionand/or from components of the exhaust system 134. Although shownseparated for purposes of illustration, the turbine 160-1 and thecompressor 160-2 may be attached to each other, placing intake air inclose proximity to hot exhaust.

The engine system 100 may include an exhaust gas recirculation (EGR)valve 170, which selectively redirects exhaust gas back to the intakemanifold 110. The EGR valve 170 may be located upstream of theturbocharger's turbine 160-1. The EGR valve 170 may be controlled by anEGR actuator module 172 based on signals from the ECM 114.

A position of the crankshaft may be measured using a crankshaft positionsensor 180. A rotational speed of the crankshaft (an engine speed) maybe determined based on the crankshaft position. A temperature of theengine coolant may be measured using an engine coolant temperature (ECT)sensor 182. The ECT sensor 182 may be located within the engine 102 orat other locations where the coolant is circulated, such as a radiator(not shown).

A pressure within the intake manifold 110 may be measured using amanifold absolute pressure (MAP) sensor 184. In various implementations,engine vacuum, which is the difference between ambient air pressure andthe pressure within the intake manifold 110, may be measured. A massflow rate of air flowing into the intake manifold 110 may be measuredusing a mass air flow (MAF) sensor 186. In various implementations, theMAF sensor 186 may be located in a housing that also includes thethrottle valve 112.

The throttle actuator module 116 may monitor the position of thethrottle valve 112 using one or more throttle position sensors (TPS)190. An ambient temperature of air being drawn into the engine 102 maybe measured using an intake air temperature (IAT) sensor 192. The enginesystem 100 may also include one or more other sensors 193, such as anambient humidity sensor, one or more knock sensors, a compressor outletpressure sensor and/or a throttle inlet pressure sensor, a wastegateposition sensor, an EGR position sensor, and/or one or more othersuitable sensors. The ECM 114 may use signals from the sensors to makecontrol decisions for the engine system 100.

The ECM 114 may communicate with a transmission control module 194 tocoordinate shifting gears in a transmission (not shown). For example,the ECM 114 may reduce engine torque during a gear shift. The ECM 114may communicate with a hybrid control module 196 to coordinate operationof the engine 102 and an electric motor 198.

The electric motor 198 may also function as a generator, and may be usedto produce electrical energy for use by vehicle electrical systemsand/or for storage in a battery. In various implementations, variousfunctions of the ECM 114, the transmission control module 194, and thehybrid control module 196 may be integrated into one or more modules.

Each system that varies an engine parameter may be referred to as anengine actuator. For example, the throttle actuator module 116 mayadjust opening of the throttle valve 112 to achieve a target throttleopening area. The spark actuator module 126 controls the spark plugs toachieve a target spark timing relative to piston TDC. The fuel actuatormodule 124 controls the fuel injectors to achieve target fuelingparameters. The phaser actuator module 158 may control the intake andexhaust cam phasers 148 and 150 to achieve target intake and exhaust camphaser angles, respectively. The EGR actuator module 172 may control theEGR valve 170 to achieve a target EGR opening area. The boost actuatormodule 164 controls the wastegate 162 to achieve a target wastegateopening area. The cylinder actuator module 120 controls cylinderdeactivation to achieve a target number of activated or deactivatedcylinders.

The ECM 114 generates the target values for the engine actuators tocause the engine 102 to generate a target engine output torque. The ECM114 generates the target values for the engine actuators using modelpredictive control, as discussed further below.

Referring now to FIG. 2, a functional block diagram of an example enginecontrol system is presented. An example implementation of the ECM 114includes a driver torque module 202, an axle torque arbitration module204, and a propulsion torque arbitration module 206. The ECM 114 mayinclude a hybrid optimization module 208. The ECM 114 also includes areserves/loads module 220, a torque requesting module 224, an aircontrol module 228, a spark control module 232, a cylinder controlmodule 236, and a fuel control module 240.

The driver torque module 202 may determine a driver torque request 254based on a driver input 255 from the driver input module 104. The driverinput 255 may be based on, for example, a position of an acceleratorpedal and a position of a brake pedal. The driver input 255 may also bebased on cruise control, which may be an adaptive cruise control systemthat varies vehicle speed to maintain a predetermined followingdistance. The driver torque module 202 may store one or more mappings ofaccelerator pedal position to target torque and may determine the drivertorque request 254 based on a selected one of the mappings.

An axle torque arbitration module 204 arbitrates between the drivertorque request 254 and other axle torque requests 256. Axle torque(torque at the wheels) may be produced by various sources including anengine and/or an electric motor. For example, the axle torque requests256 may include a torque reduction requested by a traction controlsystem when positive wheel slip is detected. Positive wheel slip occurswhen axle torque overcomes friction between the wheels and the roadsurface, and the wheels begin to slip against the road surface. The axletorque requests 256 may also include a torque increase request tocounteract negative wheel slip, where a tire of the vehicle slips in theother direction with respect to the road surface because the axle torqueis negative.

The axle torque requests 256 may also include brake management requestsand vehicle over-speed torque requests. Brake management requests mayreduce axle torque to ensure that the axle torque does not exceed theability of the brakes to hold the vehicle when the vehicle is stopped.Vehicle over-speed torque requests may reduce the axle torque to preventthe vehicle from exceeding a predetermined speed. The axle torquerequests 256 may also be generated by vehicle stability control systems.

The axle torque arbitration module 204 outputs a predicted torquerequest 257 and an immediate torque request 258 based on the results ofarbitrating between the received torque requests 254 and 256. Asdescribed below, the predicted and immediate torque requests 257 and 258from the axle torque arbitration module 204 may selectively be adjustedby other modules of the ECM 114 before being used to control the engineactuators.

In general terms, the immediate torque request 258 may be an amount ofcurrently desired axle torque, while the predicted torque request 257may be an amount of axle torque that may be needed on short notice. TheECM 114 controls the engine system 100 to produce an axle torque equalto the immediate torque request 258. However, different combinations oftarget values may result in the same axle torque. The ECM 114 maytherefore adjust the target values to enable a faster transition to thepredicted torque request 257, while still maintaining the axle torque atthe immediate torque request 258.

In various implementations, the predicted torque request 257 may be setbased on the driver torque request 254. The immediate torque request 258may be set to less than the predicted torque request 257 under somecircumstances, such as when the driver torque request 254 is causingwheel slip on an icy surface. In such a case, a traction control system(not shown) may request a reduction via the immediate torque request258, and the ECM 114 reduces the engine torque output to the immediatetorque request 258. However, the ECM 114 performs the reduction so theengine system 100 can quickly resume producing the predicted torquerequest 257 once the wheel slip stops.

In general terms, the difference between the immediate torque request258 and the (generally higher) predicted torque request 257 can bereferred to as a torque reserve. The torque reserve may represent theamount of additional torque (above the immediate torque request 258)that the engine system 100 can begin to produce with minimal delay. Fastengine actuators are used to increase or decrease current axle torquewith minimal delay. Fast engine actuators are defined in contrast withslow engine actuators.

In general terms, fast engine actuators can change the axle torque morequickly than slow engine actuators. Slow actuators may respond moreslowly to changes in their respective target values than fast actuatorsdo. For example, a slow actuator may include mechanical components thatrequire time to move from one position to another in response to achange in target value. A slow actuator may also be characterized by theamount of time it takes for the axle torque to begin to change once theslow actuator begins to implement the changed target value. Generally,this amount of time will be longer for slow actuators than for fastactuators. In addition, even after beginning to change, the axle torquemay take longer to fully respond to a change in a slow actuator.

For example only, the spark actuator module 126 may be a fast actuator.Spark-ignition engines may combust fuels including, for example,gasoline and ethanol, by applying a spark. By way of contrast, thethrottle actuator module 116 may be a slow actuator.

For example, as described above, the spark actuator module 126 can varythe spark timing for a next firing event when the spark timing ischanged between a last firing event and the next firing event. By way ofcontrast, changes in throttle opening take longer to affect engineoutput torque. The throttle actuator module 116 changes the throttleopening by adjusting the angle of the blade of the throttle valve 112.Therefore, when the target value for opening of the throttle valve 112is changed, there is a mechanical delay as the throttle valve 112 movesfrom its previous position to a new position in response to the change.In addition, air flow changes based on the throttle opening are subjectto air transport delays in the intake manifold 110. Further, increasedair flow in the intake manifold 110 is not realized as an increase inengine output torque until the cylinder 118 receives additional air inthe next intake stroke, compresses the additional air, and commences thecombustion stroke.

Using these actuators as an example, a torque reserve can be created bysetting the throttle opening to a value that would allow the engine 102to produce the predicted torque request 257. Meanwhile, the spark timingcan be set based on the immediate torque request 258, which is less thanthe predicted torque request 257. Although the throttle openinggenerates enough air flow for the engine 102 to produce the predictedtorque request 257, the spark timing is retarded (which reduces torque)based on the immediate torque request 258. The engine output torque willtherefore be equal to the immediate torque request 258.

When additional torque is needed, the spark timing can be set based onthe predicted torque request 257 or a torque between the predicted andimmediate torque requests 257 and 258. By the following firing event,the spark actuator module 126 may return the spark timing to an optimumvalue, which allows the engine 102 to produce the full engine outputtorque achievable with the air flow already present. The engine outputtorque may therefore be quickly increased to the predicted torquerequest 257 without experiencing delays from changing the throttleopening.

The axle torque arbitration module 204 may output the predicted torquerequest 257 and the immediate torque request 258 to a propulsion torquearbitration module 206. In various implementations, the axle torquearbitration module 204 may output the predicted and immediate torquerequests 257 and 258 to the hybrid optimization module 208.

The hybrid optimization module 208 may determine how much torque shouldbe produced by the engine 102 and how much torque should be produced bythe electric motor 198. The hybrid optimization module 208 then outputsmodified predicted and immediate torque requests 259 and 260,respectively, to the propulsion torque arbitration module 206. Invarious implementations, the hybrid optimization module 208 may beimplemented in the hybrid control module 196.

The predicted and immediate torque requests received by the propulsiontorque arbitration module 206 are converted from an axle torque domain(torque at the wheels) into a propulsion torque domain (torque at thecrankshaft). This conversion may occur before, after, as part of, or inplace of the hybrid optimization module 208.

The propulsion torque arbitration module 206 arbitrates betweenpropulsion torque requests 290, including the converted predicted andimmediate torque requests. The propulsion torque arbitration module 206generates an arbitrated predicted torque request 261 and an arbitratedimmediate torque request 262. The arbitrated torque requests 261 and 262may be generated by selecting a winning request from among receivedtorque requests. Alternatively or additionally, the arbitrated torquerequests may be generated by modifying one of the received requestsbased on another one or more of the received torque requests.

For example, the propulsion torque requests 290 may include torquereductions for engine over-speed protection, torque increases for stallprevention, and torque reductions requested by the transmission controlmodule 194 to accommodate gear shifts. The propulsion torque requests290 may also result from clutch fuel cutoff, which reduces the engineoutput torque when the driver depresses the clutch pedal in a manualtransmission vehicle to prevent a flare in engine speed.

The propulsion torque requests 290 may also include an engine shutoffrequest, which may be initiated when a critical fault is detected. Forexample only, critical faults may include detection of vehicle theft, astuck starter motor, electronic throttle control problems, andunexpected torque increases. In various implementations, when an engineshutoff request is present, arbitration selects the engine shutoffrequest as the winning request. When the engine shutoff request ispresent, the propulsion torque arbitration module 206 may output zero asthe arbitrated predicted and immediate torque requests 261 and 262.

In various implementations, an engine shutoff request may simply shutdown the engine 102 separately from the arbitration process. Thepropulsion torque arbitration module 206 may still receive the engineshutoff request so that, for example, appropriate data can be fed backto other torque requestors. For example, all other torque requestors maybe informed that they have lost arbitration.

The reserves/loads module 220 receives the arbitrated predicted andimmediate torque requests 261 and 262. The reserves/loads module 220 mayadjust the arbitrated predicted and immediate torque requests 261 and262 to create a torque reserve and/or to compensate for one or moreloads. The reserves/loads module 220 then outputs adjusted predicted andimmediate torque requests 263 and 264 to the torque requesting module224.

For example only, a catalyst light-off process or a cold start emissionsreduction process may require retarded spark timing. The reserves/loadsmodule 220 may therefore increase the adjusted predicted torque request263 above the adjusted immediate torque request 264 to create retardedspark for the cold start emissions reduction process. In anotherexample, the air/fuel ratio of the engine and/or the mass air flow maybe directly varied, such as by diagnostic intrusive equivalence ratiotesting and/or new engine purging. Before beginning these processes, atorque reserve may be created or increased to quickly offset decreasesin engine output torque that result from leaning the air/fuel mixtureduring these processes.

The reserves/loads module 220 may also create or increase a torquereserve in anticipation of a future load, such as power steering pumpoperation or engagement of an air conditioning (A/C) compressor clutch.The reserve for engagement of the A/C compressor clutch may be createdwhen the driver first requests air conditioning. The reserves/loadsmodule 220 may increase the adjusted predicted torque request 263 whileleaving the adjusted immediate torque request 264 unchanged to producethe torque reserve: Then, when the A/C compressor clutch engages, thereserves/loads module 220 may increase the adjusted immediate torquerequest 264 by the estimated load of the A/C compressor clutch.

The torque requesting module 224 receives the adjusted predicted andimmediate torque requests 263 and 264. The torque requesting module 224determines how the adjusted predicted and immediate torque requests 263and 264 will be achieved. The torque requesting module 224 may be enginetype specific. For example, the torque requesting module 224 may beimplemented differently or use different control schemes forspark-ignition engines versus compression-ignition engines.

In various implementations, the torque requesting module 224 may definea boundary between modules that are common across all engine types andmodules that are engine type specific. For example, engine types mayinclude spark-ignition and compression-ignition. Modules prior to thetorque requesting module 224, such as the propulsion torque arbitrationmodule 206, may be common across engine types, while the torquerequesting module 224 and subsequent modules may be engine typespecific.

The torque requesting module 224 determines an air torque request 265based on the adjusted predicted and immediate torque requests 263 and264. The air torque request 265 may be a brake torque. Brake torque mayrefer to torque at the crankshaft under the current operatingconditions.

Target values for airflow controlling engine actuators are determinedbased on the air torque request 265. More specifically, based on the airtorque request 265, the air control module 228 determines a targetwastegate opening area 266, a target throttle opening area 267, a targetEGR opening area 268, a target intake cam phaser angle 269, and a targetexhaust cam phaser angle 270. The air control module 228 determines thetarget wastegate opening area 266, the target throttle opening area 267,the target EGR opening area 268, the target intake cam phaser angle 269,and the target exhaust cam phaser angle 270 using model predictivecontrol, as discussed further below.

The boost actuator module 164 controls the wastegate 162 to achieve thetarget wastegate opening area 266. For example, a first conversionmodule 272 may convert the target wastegate opening area 266 into atarget duty cycle 274 to be applied to the wastegate 162, and the boostactuator module 164 may apply a signal to the wastegate 162 based on thetarget duty cycle 274. In various implementations, the first conversionmodule 272 may convert the target wastegate opening area 266 into atarget wastegate position (not shown), and convert the target wastegateposition into the target duty cycle 274.

The throttle actuator module 116 controls the throttle valve 112 toachieve the target throttle opening area 267. For example, a secondconversion module 276 may convert the target throttle opening area 267into a target duty cycle 278 to be applied to the throttle valve 112,and the throttle actuator module 116 may apply a signal to the throttlevalve 112 based on the target duty cycle 278. In variousimplementations, the second conversion module 276 may convert the targetthrottle opening area 267 into a target throttle position (not shown),and convert the target throttle position into the target duty cycle 278.

The EGR actuator module 172 controls the EGR valve 170 to achieve thetarget EGR opening area 268. For example, a third conversion module 280may convert the target EGR opening area 268 into a target duty cycle 282to be applied to the EGR valve 170, and the EGR actuator module 172 mayapply a signal to the EGR valve 170 based on the target duty cycle 282.In various implementations, the third conversion module 280 may convertthe target EGR opening area 268 into a target EGR position (not shown),and convert the target EGR position into the target duty cycle 282.

The phaser actuator module 158 controls the intake cam phaser 148 toachieve the target intake cam phaser angle 269. The phaser actuatormodule 158 also controls the exhaust cam phaser 150 to achieve thetarget exhaust cam phaser angle 270. In various implementations, afourth conversion module (not shown) may be included and may convert thetarget intake and exhaust cam phaser angles into target intake andexhaust duty cycles, respectively. The phaser actuator module 158 mayapply the target intake and exhaust duty cycles to the intake andexhaust cam phasers 148 and 150, respectively. In variousimplementations, the air control module 228 may determine a targetoverlap factor and a target effective displacement, and the phaseractuator module 158 may control the intake and exhaust cam phasers 148and 150 to achieve the target overlap factor and the target effectivedisplacement.

The torque requesting module 224 may also generate a spark torquerequest 283, a cylinder shut-off torque request 284, and a fuel torquerequest 285 based on the predicted and immediate torque requests 263 and264. The spark control module 232 may determine how much to retard thespark timing (which reduces engine output torque) from an optimum sparktiming based on the spark torque request 283. For example only, a torquerelationship may be inverted to solve for a target spark timing 286. Fora given torque request (T_(Req)), the target spark timing (S_(T)) 286may be determined based on:

S _(T) =f ⁻¹(T _(Req),APC,I,E,AF,OT,#),  (1)

where APC is an APC, I is an intake valve phasing value, E is an exhaustvalve phasing value, AF is an air/fuel ratio, OT is an oil temperature,and # is a number of activated cylinders. This relationship may beembodied as an equation and/or as a lookup table. The air/fuel ratio(AF) may be the actual air/fuel ratio, as reported by the fuel controlmodule 240.

When the spark timing is set to the optimum spark timing, the resultingtorque may be as close to a minimum spark advance for best torque (MBTspark timing) as possible. Best torque refers to the maximum engineoutput torque that is generated for a given air flow as spark timing isadvanced, while using fuel having an octane rating greater than apredetermined octane rating and using stoichiometric fueling. The sparktiming at which this best occurs is referred to as an MBT spark timing.The optimum spark timing may differ slightly from MBT spark timingbecause of, for example, fuel quality (such as when lower octane fuel isused) and environmental factors, such as ambient humidity andtemperature. The engine output torque at the optimum spark timing maytherefore be less than MBT. For example only, a table of optimum sparktimings corresponding to different engine operating conditions may bedetermined during a calibration phase of vehicle design, and the optimumvalue is determined from the table based on current engine operatingconditions.

The cylinder shut-off torque request 284 may be used by the cylindercontrol module 236 to determine a target number of cylinders todeactivate 287. In various implementations, a target number of cylindersto activate may be used. The cylinder actuator module 120 selectivelyactivates and deactivates the valves of cylinders based on the targetnumber 287.

The cylinder control module 236 may also instruct the fuel controlmodule 240 to stop providing fuel for deactivated cylinders and mayinstruct the spark control module 232 to stop providing spark fordeactivated cylinders. The spark control module 232 may stop providingspark to a cylinder once an fuel/air mixture that is already present inthe cylinder has been combusted.

The fuel control module 240 may vary the amount of fuel provided to eachcylinder based on the fuel torque request 285. More specifically, thefuel control module 240 may generate target fueling parameters 288 basedon the fuel torque request 285. The target fueling parameters 288 mayinclude, for example, target mass of fuel, target injection startingtiming, and target number of fuel injections.

During normal operation, the fuel control module 240 may operate in anair lead mode in which the fuel control module 240 attempts to maintaina stoichiometric air/fuel ratio by controlling fueling based on airflow. For example, the fuel control module 240 may determine a targetfuel mass that will yield stoichiometric combustion when combined with apresent mass of air per cylinder (APC).

FIG. 3 is a functional block diagram of an example implementation of theair control module 228. Referring now to FIGS. 2 and 3, as discussedabove, the air torque request 265 may be a brake torque. A torqueconversion module 304 converts the air torque request 265 from braketorque into base torque. The torque request resulting from conversioninto base torque will be referred to as a base air torque request 308.

Base torques may refer to torque at the crankshaft made during operationof the engine 102 on a dynamometer while the engine 102 is warm and notorque loads are imposed on the engine 102 by accessories, such as analternator and the A/C compressor. The torque conversion module 304 mayconvert the air torque request 265 into the base air torque request 308,for example, using a mapping or a function that relates brake torques tobase torques. In various implementations, the torque conversion module304 may convert the air torque request 265 into another suitable type oftorque, such as an indicated torque. An indicated torque may refer to atorque at the crankshaft attributable to work produced via combustionwithin the cylinders.

An MPC module 312 generates the target values 266-270 using a MPC (ModelPredictive Control) scheme. The MPC module 312 may be a single module ormay comprise multiple modules. For example, the MPC module 312 mayinclude a sequence determination module 316. The sequence determinationmodule 316 determines possible sequences of the target values 266-270that could be used together during N future control loops.

A prediction module 323 determines predicted responses of the engine 102to the possible sequences of the target values 266-270, respectively,based on a (mathematical) model 324 of the engine 102, exogenous inputs328, and feedback inputs 330. More specifically, based on a possiblesequence of the target values 266-270, the exogenous inputs 328, and thefeedback inputs 330, using the model 324, the prediction module 323generates a sequence of predicted torques of the engine 102 for the Ncontrol loops, a sequence of predicted APCs for the N control loops, asequence of predicted amounts of external dilution for the N controlloops, a sequence of predicted amounts of residual dilution for the Ncontrol loops, a sequence of predicted combustion phasing values for theN control loops, and a sequence of predicted combustion quality valuesfor the N control loops.

The model 324 may be, for example, a function or a mapping calibratedbased on characteristics of the engine 102. Dilution may refer to anamount of exhaust from a prior combustion event trapped within acylinder for a combustion event. External dilution may refer to exhaustprovided for a combustion event via the EGR valve 170. Residual dilution(also referred to as internal dilution) may refer to exhaust thatremains in a cylinder and/or exhaust that is pushed back into thecylinder following the exhaust stroke of a combustion cycle.

Combustion phasing may refer to a crankshaft position where apredetermined amount of fuel injected is combusted within a cylinderrelative to a predetermined crankshaft position for combustion of thepredetermined amount of injected fuel. For example, combustion phasingmay be expressed in terms of CA50 relative to a predetermined CA50. CA50may refer to a crankshaft angle (CA) where 50 percent of a mass ofinjected fuel has been combusted within a cylinder. The predeterminedCA50 may correspond to a CA50 where a maximum amount of work is producedfrom the fuel injected and may be approximately 8.5-approximately 10degrees after TDC (top dead center) in various implementations. Whilecombustion phasing will be discussed in terms of CA50 values, anothersuitable parameter indicative of combustion phasing may be used.Additionally, while combustion quality will be discussed as coefficientof variation (COV) of indicated mean effective pressure (IMEP) values,another suitable parameter indicative of combustion quality may be used.

The exogenous inputs 328 may include parameters that are not directlyaffected by the throttle valve 112, the EGR valve 170, the turbocharger,the intake cam phaser 148, and the exhaust cam phaser 150. For example,the exogenous inputs 328 may include engine speed, turbocharger inletair pressure, IAT, and/or one or more other parameters. The feedbackinputs 330 may include, for example, an estimated torque output of theengine 102, an exhaust pressure downstream of the turbine 160-1 of theturbocharger, the IAT, an APC of the engine 102, an estimated residualdilution, an estimated external dilution, and/or one or more othersuitable parameters. The feedback inputs 330 may be measured usingsensors (e.g., the IAT) and/or estimated based on one or more otherparameters.

Each of the possible sequences identified by the sequence determinationmodule 316 includes one sequence of N values for each of the targetvalues 266-270. In other words, each possible sequence includes asequence of N values for the target wastegate opening area 266, asequence of N values for the target throttle opening area 267, asequence of N values for the target EGR opening area 268, a sequence ofN values for the target intake cam phaser angle 269, and a sequence of Nvalues for the target exhaust cam phaser angle 270. Each of the N valuesare for a corresponding one of the N future control loops. N is aninteger greater than or equal to one.

A cost module 332 determines a cost value for each of the possiblesequences of the target values 266-270 based on the predicted parametersdetermined for a possible sequence and output reference values 356. Anexample cost determination is discussed further below.

A selection module 344 selects one of the possible sequences of thetarget values 266-270 based on the costs of the possible sequences,respectively. For example, the selection module 344 may select the oneof the possible sequences having the lowest cost while satisfyingactuator constraints 348 and output constraints 352. In variousimplementations, the model 324 may select the one of the possiblesequences having the lowest cost while satisfying the actuatorconstraints 348 and the output constraints 352.

In various implementations, satisfaction of the actuator constraints 348and the output constraints may be considered in the cost determination.In other words, the cost module 332 may determine the cost valuesfurther based on the actuator constraints 348 and the output constraints352. As discussed further below, based on how the cost values aredetermined, the selection module 344 will select the one of the possiblesequences that best achieves the base air torque request 308 whileminimizing the APC, subject to the actuator constraints 348 and theoutput constraints 352.

The selection module 344 may set the target values 266-270 to the firstones of the N values of the selected possible sequence, respectively. Inother words, the selection module 344 may set the target wastegateopening area 266 to the first one of the N values in the sequence of Nvalues for the target wastegate opening area 266, set the targetthrottle opening area 267 to the first one of the N values in thesequence of N values for the target throttle opening area 267, set thetarget EGR opening area 268 to the first one of the N values in thesequence of N values for the target EGR opening area 268, set the targetintake cam phaser angle 269 to the first one of the N values in thesequence of N values for the target intake cam phaser angle 269, and setthe target exhaust cam phaser angle 270 to the first one of the N valuesin the sequence of N values for the target exhaust cam phaser angle 270.

During a next control loop, the MPC module 312 identifies possiblesequences, generates the predicted parameters for the possiblesequences, determines the cost of each of the possible sequences,selects of one of the possible sequences, and sets of the target values266-270 to the first set of the target values 266-270 in the selectedpossible sequence. This process continues for each control loop.

An actuator constraint module 360 (see FIG. 2) sets one of the actuatorconstraints 348 for each of the target values 266-270. In other words,the actuator constraint module 360 sets an actuator constraint for thethrottle valve 112, an actuator constraint for the EGR valve 170, anactuator constraint for the wastegate 162, an actuator constraint forthe intake cam phaser 148, and an actuator constraint for the exhaustcam phaser 150.

The actuator constraints 348 for each one of the target values 266-270may include a maximum value for an associated target value and a minimumvalue for that target value. The actuator constraint module 360 maygenerally set the actuator constraints 348 to predetermined operationalranges for the associated actuators. More specifically, the actuatorconstraint module 360 may generally set the actuator constraints 348 topredetermined operational ranges for the throttle valve 112, the EGRvalve 170, the wastegate 162, the intake cam phaser 148, and the exhaustcam phaser 150, respectively.

However, the actuator constraint module 360 may selectively adjust oneor more of the actuator constraints 348 under some circumstances. Forexample, the actuator constraint module 360 may adjust the actuatorconstraints for a given actuator to narrow the operational range forthat engine actuator when a fault is diagnosed in that engine actuator.For another example only, the actuator constraint module 360 may adjustthe actuator constraints such that the target value for a given actuatorfollows a predetermined schedule over time or changes by a predeterminedamount, for example, for a fault diagnostic, such as a cam phaser faultdiagnostic, a throttle diagnostic, an EGR diagnostic, etc. For a targetvalue to follow a predetermined schedule over time or to change by apredetermined amount, the actuator constraint module 360 may set theminimum and maximum values to the same value. The minimum and maximumvalues being set to the same value may force the corresponding targetvalue to be set to the same value as the minimum and maximum values. Theactuator constraint module 360 may vary the same value to which theminimum and maximum values are set over time to cause the target valueto follow a predetermined schedule.

An output constraint module 364 (see FIG. 2) sets the output constraints352 for the predicted torque output of the engine 102, the predictedCA50, the predicted COV of IMEP, the predicted residual dilution, andthe predicted external dilution. The output constraints 352 for each oneof the predicted values may include a maximum value for an associatedpredicted parameter and a minimum value for that predicted parameter.For example, the output constraints 352 may include a minimum torque, amaximum torque, a minimum CA50 and a maximum CA50, a minimum COV of IMEPand a maximum COV of IMEP, a minimum residual dilution and a maximumresidual dilution, and a minimum external dilution and a maximumexternal dilution.

The output constraint module 364 may generally set the outputconstraints 352 to predetermined ranges for the associated predictedparameters, respectively. However, the output constraint module 364 mayvary one or more of the output constraints 352 under some circumstances.For example, the output constraint module 364 may retard the maximumCA50, such as when knock occurs within the engine 102. For anotherexample, the output constraint module 364 may increase the maximum COVof IMEP under low load conditions, such as during engine idling wherethe a higher COV of IMEP may be needed to achieve a given torquerequest.

A reference module 368 (see FIG. 2) generates the reference values 356for the target values 266-270, respectively. The reference values 356include a reference for each of the target values 266-270. In otherwords, the reference values 356 include a reference wastegate openingarea, a reference throttle opening area, a reference EGR opening area, areference intake cam phaser angle, and a reference exhaust cam phaserangle.

The reference module 368 may determine the reference values 356, forexample, based on the air torque request 265, the base air torquerequest 308, and/or one or more other suitable parameters. The referencevalues 356 provide references for setting the target values 266-270,respectively. The reference values 356 may be used to determine the costvalues for possible sequences. The reference values 356 may also be usedfor one or more other reasons, such as by the sequence determinationmodule 316 to determine possible sequences.

Instead of or in addition to generating sequences of possible targetvalues and determining the cost of each of the sequences, the MPC module312 may identify a sequence of possible target values having the lowestcost using convex optimization techniques. For example, the MPC module312 may determine the target values 266-270 using a quadraticprogramming (QP) solver, such as a Dantzig QP solver. In anotherexample, the MPC module 312 may generate a surface of cost values forthe possible sequences of the target values 266-270 and, based on theslope of the cost surface, identify a set of possible target valueshaving the lowest cost. The MPC module 312 may then test that set ofpossible target values to determine whether that set of possible targetvalues will satisfy the actuator constraints 348 and the outputconstraints 352. The MPC module 312 selects the set of possible targetvalues having the lowest cost while satisfying the actuator constraints348 and the output constraints 352.

The cost module 332 may determine the cost for the possible sequences ofthe target values 266-270 based on relationships between: the predictedtorque and the base air torque request 308; the predicted APC and zero;the possible target values and the respective actuator constraints 348;the other predicted parameters and the respective output constraints352; and the possible target values and the respective reference values356. The relationships may be weighted, for example, to control theeffect that each of the relationships has on the cost.

For example only, the cost module 332 may determine the cost for apossible sequence of the target values 266-270 based on the equation:

Cost=Σ_(i=1) ^(N)ρε² +∥wT*(TP _(i)−BATR)∥² +∥wA*(APCP _(i)−0)∥²,

where Cost is the cost for the possible sequence of the target values266-270, TPi is the predicted torque of the engine 102 for an i-th oneof the N control loops, BATR is the base air torque request 308, and wTis a weighting value associated with the relationship between thepredicted and reference engine torques. APCPi is a predicted APC for thei-th one of the N control loops and wA is a weighting value associatedwith the relationship between the predicted APC and zero.

The cost module 332 may determine the cost for a possible sequence ofthe target values 266-270 based on the following more detailed equation:

Cost=Σ_(i=1) ^(N)ρε² +∥wT*(TP _(i)−BATR)∥² +∥wA*(APCP _(i)−0)∥²∥wTV*(PTTOi−TORef)∥² +∥wWG*(PTWGOi−EGORef)∥² +∥wEGR*(PTEGROi−EGRORef)∥²+∥wIP*(PTICPi−ICPRef)∥² +∥wEP*(PTECPi−ECPRef)∥²,

subject to the actuator constraints 348 and the output constraints 352.Cost is the cost for the possible sequence of the target values 266-270,TPi is the predicted torque of the engine 102 for an i-th one of the Ncontrol loops, BATR is the base air torque request 308, and wT is aweighting value associated with the relationship between the predictedand reference engine torques. APCPi is a predicted APC for the i-th oneof the N control loops and wA is a weighting value associated with therelationship between the predicted APC and zero.

PTTOi is a possible target throttle opening for the i-th one of the Ncontrol loops, TORef is the reference throttle opening, and wTV is aweighting value associated with the relationship between the possibletarget throttle openings and the reference throttle opening. PTWGOi is apossible target wastegate opening for the i-th one of the N controlloops, WGORef is the reference wastegate opening, and wWG is a weightingvalue associated with the relationship between the possible targetwastegate openings and the reference wastegate opening.

PTEGROi is a possible target EGR opening for the i-th one of the Ncontrol loops, EGRRef is the reference EGR opening, and wEGR is aweighting value associated with the relationship between the possibletarget EGR openings and the reference EGR opening. PTICi is a possibletarget intake cam phaser angle for the i-th one of the N control loops,ICPRef is the reference intake cam phaser angle, and wIP is a weightingvalue associated with the relationship between the possible targetintake cam phaser angle and the reference intake cam phaser angle. PTECiis a possible target exhaust cam phaser angle for the i-th one of the Ncontrol loops, ECPRef is the reference exhaust cam phaser angle, and wEPis a weighting value associated with the relationship between thepossible target exhaust cam phaser angle and the reference exhaust camphaser angle.

ρ is a weighting value associated with satisfaction of the outputconstraints 352. ε is a variable that the cost module 332 may set basedon whether the output constraints 352 will be satisfied. For example,the cost module 332 may increase E when a predicted parameter is greaterthan or less than the corresponding minimum or maximum value (e.g., byat least a predetermined amount). The cost module 332 may set Eε to zerowhen all of the output constraints 352 are satisfied. ρ may be greaterthan the weighting value wT, the weighting value WA, and the otherweighting values (wTV, wWG, wEGR, wIP, wEP) such that the costdetermined for a possible sequence will be large if one or more of theoutput constraints 352 are not satisfied. This may help preventselection of a possible sequence where one or more of the outputconstraints 352 are not satisfied.

The weighting value wT may be greater than the weighting value wA andthe weighting values wTV, wWG, wEGR, wIP, and wEP. In this manner, therelationship between the relationship between the predicted enginetorque and the base air torque request 308 have a larger effect on thecost and, therefore, the selection of one of the possible sequences asdiscussed further below. The cost increases as the difference betweenthe predicted engine torque and the base air torque request 308increases and vice versa.

The weighting value wA may be less than the weighting value wT andgreater than the weighting values wTV, wWG, wEGR, wIP, and wEP. In thismanner, the relationship between the predicted APC and zero has a largeeffect on the cost, but less than the relationship between the predictedengine torque and the base air torque request 308. The cost increases asthe difference between the predicted APC and zero increases and viceversa. While the example use of zero is shown and has been discussed, apredetermined minimum APC may be used in place of zero.

Determining the cost based on the difference between the predicted APCand zero therefore helps ensure that the APC will be minimized.Decreasing APC decreases fuel consumption as fueling is controlled basedon the actual APC to achieve a target air/fuel mixture. As the selectionmodule 344 may select the one of the possible sequences having thelowest cost, the selection module 344 may select the one of the possiblesequences that best achieves the base air torque request 308 whileminimizing the APC.

The weighting values wTV, wWG, wEGR, wIP, and wEP may be less than allof the other weighting values. In this manner, during steady-stateoperation, the target values 266-270 may settle near or at the referencevalues 356, respectively. During transient operation, however, the MPCmodule 312 may adjust the target values 266-270 away from the referencevalues 356 in order to achieve the base air torque request 308, whileminimizing the APC and satisfying the actuator constraints 348 and theoutput constraints 352.

In operation, the MPC module 312 may determine the cost values for thepossible sequences. The MPC module 312 may then select the one of thepossible sequences having the lowest cost. The MPC module 312 may nextdetermine whether the selected possible sequence satisfies the actuatorconstraints 348. If so, the possible sequence may be used. If not, theMPC module 312 determines, based on the selected possible sequence, apossible sequence that satisfies the actuator constraints 348 and thathas the lowest cost. The MPC module 312 may use the possible sequencethat satisfies the actuator constraints 348 and that has the lowestcost.

Referring now to FIG. 4, a flowchart depicting an example method ofcontrolling the throttle valve 112, the intake cam phaser 148, theexhaust cam phaser 150, the wastegate 162 (and therefore theturbocharger), and the EGR valve 170 using MPC (model predictivecontrol) is presented. Control may begin with 404 where the torquerequesting module 224 determines the air torque request 265 based on theadjusted predicted and immediate torque requests 263 and 264.

At 408, the torque conversion module 304 may convert the air torquerequest 265 into the base air torque request 308 or into anothersuitable type of torque for use by the MPC module 312. The sequencedetermination module 316 determines possible sequences of the targetvalues 266-270 based on the base air torque request 308 at 412.

At 416, the prediction module 323 determines the predicted parametersfor each of the possible sequences of target values. The predictionmodule 323 determines the predicted parameters for the possiblesequences based on the model 324 of the engine 102, the exogenous inputs328, and the feedback inputs 330. More specifically, based on a possiblesequence of the target values 266-270, the exogenous inputs 328, and thefeedback inputs 330, using the model 324, the prediction module 323generates a sequence of predicted torques of the engine 102 for the Ncontrol loops, a sequence of predicted APCs for the N control loops, asequence of predicted amounts of external dilution for the N controlloops, a sequence of predicted amounts of residual dilution for the Ncontrol loops, a sequence of predicted combustion phasing values for theN control loops, and a sequence of predicted combustion quality valuesfor the N control loops.

The cost module 332 determines the costs for the possible sequences,respectively, at 420. For example only, the cost module 332 maydetermine the cost for a possible sequence of the target values 266-270based on the equation

Cost=Σ_(i=1) ^(N)ρε² +∥wT*(TP _(i)−BATR)∥² +∥wA*(APCP _(i)−0)∥²,

or based on the equation

Cost=Σ_(i=1) ^(N)ρε² +∥wT*(TP _(i)−BATR)∥² +∥wA*(APCP _(i)−0)∥²+∥wTV*(PTTOi−TORef)∥² +∥wWG*(PTWGOi−EGORef)∥² +∥wEGR*(PTEGROi−EGRORef)∥²+∥wIP*(PTICPi−ICPRef)∥² +∥wEP*(PTECPi−ECPRef)∥²,

subject to the actuator constraints 348 and the output constraints 352,as discussed above.

The selection module 344 selects one of the possible sequences of thetarget values 266-270 based on the costs of the possible sequences,respectively, at 424. For example, the selection module 344 may selectthe one of the possible sequences having the lowest cost whilesatisfying the actuator constraints 348 and the output constraints 352.The selection module 344 may therefore select the one of the possiblesequences that best achieves the base air torque request 308 whileminimizing the APC and satisfying the output constraints 352. Instead ofor in addition to determining possible sequences of the target values230-244 at 412 and determining the cost of each of the sequences at 420,the MPC module 312 may identify a sequence of possible target valueshaving the lowest cost using convex optimization techniques as discussedabove.

The MPC module 312 may determine whether the selected one of thepossible sequences satisfies the actuator constraints 348 at 425. If 425is true, control may continue with 428. If 425 is false, the MPC module312 may determine, based on the selected possible sequence, a possiblesequence that satisfies the actuator constraints 348 and that has thelowest cost at 426, and control may continue with 428. The possiblesequence that satisfies the actuator constraints 348 and that has thelowest cost may be used, as discussed below.

At 428, the first conversion module 272 converts the target wastegateopening area 266 into the target duty cycle 274 to be applied to thewastegate 162, the second conversion module 276 converts the targetthrottle opening area 267 into the target duty cycle 278 to be appliedto the throttle valve 112. The third conversion module 280 also convertsthe target EGR opening area 268 into the target duty cycle 282 to beapplied to the EGR valve 170 at 428. The fourth conversion module mayalso convert the target intake and exhaust cam phaser angles 269 and 270into the target intake and exhaust duty cycles to be applied to theintake and exhaust cam phasers 148 and 150, respectively.

At 432, the throttle actuator module 116 controls the throttle valve 112to achieve the target throttle opening area 267, and the phaser actuatormodule 158 controls the intake and exhaust cam phasers 148 and 150 toachieve the target intake and exhaust cam phaser angles 269 and 270,respectively. For example, the throttle actuator module 116 may apply asignal to the throttle valve 112 at the target duty cycle 278 to achievethe target throttle opening area 267. Also at 432, the EGR actuatormodule 172 controls the EGR valve 170 to achieve the target EGR openingarea 268, and the boost actuator module 164 controls the wastegate 162to achieve the target wastegate opening area 266. For example, the EGRactuator module 172 may apply a signal to the EGR valve 170 at thetarget duty cycle 282 to achieve the target EGR opening area 268, andthe boost actuator module 164 may apply a signal to the wastegate 162 atthe target duty cycle 274 to achieve the target wastegate opening area266. While FIG. 4 is shown as ending after 432, FIG. 4 may beillustrative of one control loop, and control loops may be executed at apredetermined rate.

The foregoing description is merely illustrative in nature and is in noway intended to limit the disclosure, its application, or uses. Thebroad teachings of the disclosure can be implemented in a variety offorms. Therefore, while this disclosure includes particular examples,the true scope of the disclosure should not be so limited since othermodifications will become apparent upon a study of the drawings, thespecification, and the following claims. As used herein, the phrase atleast one of A, B, and C should be construed to mean a logical (A or Bor C), using a non-exclusive logical OR. It should be understood thatone or more steps within a method may be executed in different order (orconcurrently) without altering the principles of the present disclosure.

In this application, including the definitions below, the term modulemay be replaced with the term circuit. The term module may refer to, bepart of, or include an Application Specific Integrated Circuit (ASIC); adigital, analog, or mixed analog/digital discrete circuit; a digital,analog, or mixed analog/digital integrated circuit; a combinationallogic circuit; a field programmable gate array (FPGA); a processor(shared, dedicated, or group) that executes code; memory (shared,dedicated, or group) that stores code executed by a processor; othersuitable hardware components that provide the described functionality;or a combination of some or all of the above, such as in asystem-on-chip.

The term code, as used above, may include software, firmware, and/ormicrocode, and may refer to programs, routines, functions, classes,and/or objects. The term shared processor encompasses a single processorthat executes some or all code from multiple modules. The term groupprocessor encompasses a processor that, in combination with additionalprocessors, executes some or all code from one or more modules. The termshared memory encompasses a single memory that stores some or all codefrom multiple modules. The term group memory encompasses a memory that,in combination with additional memories, stores some or all code fromone or more modules. The term memory may be a subset of the termcomputer-readable medium. The term computer-readable medium does notencompass transitory electrical and electromagnetic signals propagatingthrough a medium, and may therefore be considered tangible andnon-transitory. Non-limiting examples of a non-transitory tangiblecomputer readable medium include nonvolatile memory, volatile memory,magnetic storage, and optical storage.

The apparatuses and methods described in this application may bepartially or fully implemented by one or more computer programs executedby one or more processors. The computer programs includeprocessor-executable instructions that are stored on at least onenon-transitory tangible computer readable medium. The computer programsmay also include and/or rely on stored data.

What is claimed is:
 1. An engine control system for a vehicle,comprising: a prediction module that generates a first predicted engineoutput torque and a first predicted mass of air per cylinder (APC) basedon a model of the spark ignition engine and a first set of possibletarget values determined based on an engine torque request and thatgenerates a second predicted engine output torque and a second predictedmass of APC based on the model of the spark ignition engine and a secondset of possible target values determined based on the engine torquerequest; a cost module that: determines a first cost for the first setof possible target values based on a first predetermined weightingvalue, the first predicted engine output torque, the engine torquerequest, a second predetermined weighting value, and the first predictedmass of APC; and determines a second cost for the second set of possibletarget values based on the first predetermined weighting value, thesecond predicted engine output torque, the engine torque request, thesecond predetermined weighting value, and the second predicted mass ofAPC; a selection module that selects one of the first and second setsbased on the first and second costs and that sets target values based onthe possible target values of the selected one of the first and secondsets; and a throttle actuator module that controls opening of a throttlevalve based on a first one of the target values.
 2. The engine controlsystem of claim 1 further comprising: a boost actuator module thatcontrols opening of a wastegate of a turbocharger based on a second oneof the target values; an exhaust gas recirculation (EGR) actuator modulethat controls opening of an EGR valve based on a third one of the targetvalues; and a phaser actuator module that controls intake and exhaustvalve phasing based on fourth and fifth ones of the target values. 3.The engine control system of claim 1 wherein the cost module: determinesthe first cost based on: a first product of the first predeterminedweighting value and a magnitude of a first difference between the firstpredicted engine output torque and the engine torque request; and asecond product of the second predetermined weighting value and a seconddifference between the first predicted mass of APC and a predeterminedminimum APC; and determines the second cost based on: a third product ofthe first weighting value and a magnitude of a third difference betweenthe second predicted engine output torque and the engine torque request;and a fourth product of the second weighting value and a magnitude of afourth difference between the second predicted mass of APC and thepredetermined minimum APC.
 4. The engine control system of claim 3wherein the cost module: determines the first cost based on a sum of thefirst and second products; and determines the second cost based on a sumof the third and fourth products.
 5. The engine control system of claim3 wherein the first predetermined weighting value is greater than thesecond predetermined weighting value.
 6. The engine control system ofclaim 1 wherein the selection module selects the first set when thefirst cost is less than the second cost, and the selection moduleselects the second set when the second cost is less than the first cost.7. The engine control system of claim 1 wherein the cost module:determines the first cost further based on a third predeterminedweighting value, a first predicted crankshaft angle where apredetermined percent of injected fuel will be burned, a predeterminedminimum crankshaft angle, and a predetermined maximum crankshaft angle;and determines the second cost further based on the third predeterminedweighting value, a second predicted crankshaft angle where thepredetermined percent of injected fuel will be burned, the predeterminedminimum crankshaft angle, and the predetermined maximum crankshaftangle.
 8. The engine control system of claim 7 wherein the predictionmodule further: generates the first predicted crankshaft angle based onthe model of the spark ignition engine and the first set of possibletarget values; and generates the second predicted crankshaft angle basedon the model of the spark ignition engine and the second set of possibletarget values.
 9. The engine control system of claim 1 wherein the costmodule: determines the first cost further based on a fourthpredetermined weighting value, a first predicted coefficient ofvariation (COV) of indicated mean effective pressure (IMEP), apredetermined minimum COV of IMEP, and a predetermined maximum COV ofIMEP; and determines the second cost further based on the fourthpredetermined weighting value, a second predicted COV of IMEP, thepredetermined minimum COV of IMEP, and the predetermined maximum COV ofIMEP.
 10. The engine control system of claim 9 wherein the predictionmodule further: generates the first predicted COV of IMEP based on themodel of the spark ignition engine and the first set of possible targetvalues; and generates the second predicted COV of IMEP based on themodel of the spark ignition engine and the second set of possible targetvalues.
 11. An engine control method for a vehicle, comprising:generating a first predicted engine output torque and a first predictedmass of air per cylinder (APC) based on a model of the spark ignitionengine and a first set of possible target values determined based on anengine torque request; generating a second predicted engine outputtorque and a second predicted mass of APC based on the model of thespark ignition engine and a second set of possible target valuesdetermined based on the engine torque request; determining a first costfor the first set of possible target values based on a firstpredetermined weighting value, the first predicted engine output torque,the engine torque request, a second predetermined weighting value, andthe first predicted mass of APC; determining a second cost for thesecond set of possible target values based on the first predeterminedweighting value, the second predicted engine output torque, the enginetorque request, the second predetermined weighting value, and the secondpredicted mass of APC; selecting one of the first and second sets basedon the first and second costs; setting target values based on thepossible target values of the selected one of the first and second sets;and controlling opening of a throttle valve based on a first one of thetarget values.
 12. The engine control method of claim 11 furthercomprising: controlling opening of a wastegate of a turbocharger basedon a second one of the target values; controlling opening of an exhaustgas recirculation (EGR) valve based on a third one of the target values;and controlling intake and exhaust valve phasing based on fourth andfifth ones of the target values.
 13. The engine control method of claim11 further comprising: determining the first cost based on: a firstproduct of the first predetermined weighting value and a magnitude of afirst difference between the first predicted engine output torque andthe engine torque request; and a second product of the secondpredetermined weighting value and a second difference between the firstpredicted mass of APC and a predetermined minimum APC; and determiningthe second cost based on: a third product of the first weighting valueand a magnitude of a third difference between the second predictedengine output torque and the engine torque request; and a fourth productof the second weighting value and a magnitude of a fourth differencebetween the second predicted mass of APC and the predetermined minimumAPC.
 14. The engine control method of claim 13 further comprising:determining the first cost based on a sum of the first and secondproducts; and determining the second cost based on a sum of the thirdand fourth products.
 15. The engine control method of claim 13 whereinthe first predetermined weighting value is greater than the secondpredetermined weighting value.
 16. The engine control method of claim 11further comprising: selecting the first set when the first cost is lessthan the second cost; and selecting the second set when the second costis less than the first cost.
 17. The engine control method of claim 11further comprising: determining the first cost further based on a thirdpredetermined weighting value, a first predicted crankshaft angle wherea predetermined percent of injected fuel will be burned, a predeterminedminimum crankshaft angle, and a predetermined maximum crankshaft angle;and determining the second cost further based on the third predeterminedweighting value, a second predicted crankshaft angle where thepredetermined percent of injected fuel will be burned, the predeterminedminimum crankshaft angle, and the predetermined maximum crankshaftangle.
 18. The engine control method of claim 17 further comprising:generating the first predicted crankshaft angle based on the model ofthe spark ignition engine and the first set of possible target values;and generating the second predicted crankshaft angle based on the modelof the spark ignition engine and the second set of possible targetvalues.
 19. The engine control method of claim 11 further comprising:determining the first cost further based on a fourth predeterminedweighting value, a first predicted coefficient of variation (COV) ofindicated mean effective pressure (IMEP), a predetermined minimum COV ofIMEP, and a predetermined maximum COV of IMEP; and determining thesecond cost further based on the fourth predetermined weighting value, asecond predicted COV of IMEP, the predetermined minimum COV of IMEP, andthe predetermined maximum COV of IMEP.
 20. The engine control method ofclaim 19 further comprising: generating the first predicted COV of IMEPbased on the model of the spark ignition engine and the first set ofpossible target values; and generating the second predicted COV of IMEPbased on the model of the spark ignition engine and the second set ofpossible target values.